I needed some Tranya. A friend said "just replicate it." I looked 10 times, but i DON'T have that in my inventory replicator list. He did, so he gave me one. He was surprised I did not have it. So... Replicator menu is obviously different between players. Can I affect what is in the list somehow? I don't ever need to make cat food, but there it is anyway...

Not all-inclusive lists, but the wiki articles give you a good idea of what you can replicate with each particular chef or bartender (plusDathan the unique very rare Biochemist, who lets you replicate Ketracel White)

You need to have the Rulian Mazan Purple DOff in order to unlock Tranya.

Rulian is only available from the Investigate Temporal Anomaly assignment, which is rare and not repeatable (i.e. if you accidentally sell or dismiss Rulian after the assignment, you'll never get her back)

Do you simply have to own the DOff to open those specific permissions?

Yes, they just need to be in your roster.

The exception was Dathan, who had to be slotted in active duty in order to replicate Ketracel White, but I believe they changed that requirement. Wiki still says he has to be slotted, though, so maybe they changed it back.

I was not looking forward to replicating 1000 Cardassian tasper eggs one at a time, but I was a bit disappointed when that starbase chef requirement changed. My purple Cardie chef was making me a good amount of EC up to that point.